Two building site teams each had 10 workers. The back-to-back stem-and-leaf diagram shows the hours each worker logged in one week. Team A Stem Team B 8 5 4...
Question 1 Report
Two building site teams each had 10 workers. The back-to-back stem-and-leaf diagram shows the hours each worker logged in one week.
| Team A | Stem | Team B |
|---|---|---|
| 8 5 4 2 | 2 | 0 3 6 9 |
| 8 5 3 1 | 3 | 0 2 4 7 9 |
| 4 1 | 4 | 2 |
| Key: Team A 2 | 2 means 22 hours; Team B 2 | 0 means 20 hours | ||
- Write down the median hours for Team A. (1)
- Write down the median hours for Team B. (1)
- A bonus is paid to any team whose median exceeds 31 hours. State which team, if any, qualifies, giving a reason. (1)
- A report claimed Team A logged 320 hours, but omitted 2 extra workers who each logged 20 hours. Using the diagram, work out the true total for Team A. (1)
Answer Details
This question tests reading two sets of data from a back-to-back stem-and-leaf diagram, finding each team's median, comparing them against a bonus threshold, and correcting a total for omitted workers.
(a) Team A's ten hours, read from the diagram and placed in order, are 22, 24, 25, 28, 31, 33, 35, 38, 41, 44. With 10 values, the median is the mean of the 5th and 6th values:
\[ \frac{31+33}{2} = 32 \text{ hours} \] [1 mark]
(b) Team B's ten hours in order are 20, 23, 26, 29, 30, 32, 34, 37, 39, 42, giving a median of
\[ \frac{30+32}{2} = 31 \text{ hours} \] [1 mark]
(c) The bonus requires a median exceeding 31 hours. Team A's median of 32 hours exceeds 31, but Team B's median of exactly 31 hours does not, so only Team A qualifies for the bonus. [1 mark]
(d) Adding all ten of Team A's logged hours from the diagram gives 321 hours. Including the 2 extra workers who each logged 20 hours but were omitted from the report,
\[ 321 + (2 \times 20) = 361 \text{ hours} \] [1 mark]
The reported total of 320 hours in part (d)'s scenario is close to, but not exactly, the diagram's own total of 321 hours; either way, the two extra workers' 40 hours must still be added on top of whichever total is being corrected.
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